Not really (as for "no real evidence.") A bayonet that was recovered 800 feet from the crime scene that the pathologist said matches the victim's head wounds (including the triangular bludgeoning wounds.)
The cops, including a big city detective who investigated thousands of homicides in his career, said they couldn't think of one other case where a bayonet was used to murder a civilian.
You have a psychopath suspect who was raised a block from Percy's house and arrested six months after the crime for possession of 70 tons of military weaponry including numerous bayonets.
Documents written to him by his sibling reveal a penchant for said psycho to return to Kenilworth, where he was "always causing trouble."
Entry to the house was by someone who seemed to care not whether he was heard (and he was), which resulted in him being seen by a witness. That was reckless by any sane person's standards and the witnesses description matches the psycho's hair color, build and height (the last considering he was described as leaning over a bed.) The doctor who saw the crime scene said whoever did it was psycho.
The psycho was later shot five times by his wife, who said he'd confessed to successfully plotting another murder on Chicago's North Shore (which included Percy's neighborhood) and personally committing two other murders, including one in the spring of '66. She also said he attempted to kill his parents and make it look like a murder suicide. That took place in April '66 (IIRC) and is documented in police records.
The wife was exonerated for his killing. There is no doubt the murders and attempted murders he is said to have confessed to did occur, only he was not arrested for them which indicates his was either very lucky or clever or both.